There are a number of table or role-playing games in which the outcome of a battle or other contest is determined by comparing the relative strengths of the sides, referring to a table of odds according to the rules of the game, and creating a random number (e.g. by rolling one or more dice). For example, in battle games such as Panzer Leader or Kingmaker, a combat table is provided listing an array of odds from 1-4 (one to four) to 4-1 (four to one) on one axis, and an array of die rolls on the other axis. Given an odds number and a die roll, the outcome of the battle can be read from the appropriate cell of the table. In a battle situation, the respective strengths of the attacking force and the defending force are determined, and the ratio of the attacking strength to the defending strength is calculated. If that ratio matches one of the ratios in the combat table, then a roll can be made and the outcome found in the table.
If, however, the actual ratio in the given battle does not match a ratio in the table, then game rules round the actual ratio down to a ratio in the table. Thus, if the value of the offensive strength is 11 and the value of the defensive strength is 10, the ratio of offensive strength to defensive strength is 11/10, or 1.1. Given a table that includes columns for odds of 1-2, 1-1, and 2-1 (and perhaps larger or smaller, but not intermediate odds), the actual ratio of 1.1 (e.g., 1.1 to 1 or 11 to 10) is not in the table. The actual ratio is then rounded down to 1 to 1, which is an odds-value given in the table. The full offensive strength is therefore ignored in calculating the outcome of the battle. A more lopsided result obtains where the offensive strength-value is 19 and the defensive strength-value is 10. The actual ratio in such a case is 19/10 or 1.9, but by rounding down the odds-value in the combat table that is used remains 1-1. A single unit of defensive strength thus can have an inordinate effect simply due to the limitations of the combat table.
Further, it can be time-consuming to go through the calculation and comparison of these strength-value ratios, whether on paper or in one's head, many times during a game session, especially if some odds-value ratios in a table are not simple (e.g., 5 to 4, 3 to 2, etc.). For each battle, a ratio in the form of a fraction or decimal must be calculated, and then compared to a discrete set of odds. The odds must be considered as fractions (e.g., two to one is equivalent to 2/1 or 2, while one to two is equivalent to 1/2), and then the ratio of strengths is compared to those “fractionalized” odds. The odds to be used are the set next lower than the ratio of strengths. While an occupational hazard of participating in such games, the time and mental agility required to compare such fractions can be substantial.
Accordingly, fairer and/or easier ways to determine the outcome of battles or other odds-dependent issues in games are desirable.